The crossover in kinetic roughening of thin films from a particle-character-dominated regime to continuous growth behavior has been observed in this work. This has been accomplished by atomic force microscopy investigations of pulsed laser deposited amorphous organic films with thicknesses ranging from several nanometers to more than 4 microm. The early-stage random-deposition-like processes end once a closed layer is formed, which grows without saturation on the characteristic length scales. In addition, the influence of oblique film deposition has been examined and interpreted.